The List Total Colouring Conjecture is False

We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin–Kostochka–Woodall, Juvan–Mohar–Škrekovski and Hilton–Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.